Metastable states in glassy systems

Truly stable metastable states are an artifact of the mean-field approximation or the zero-temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs to cast them in a form involving states with finite lifetimes. Starting from elementary examples and using the results of Gaveau and Schulman, we propose a simple expression for the configurational entropy and revisit the question of taking flat averages over metastable states. The construction is applicable to finite-dimensional systems, and we explicitly show that for simple mean-field glass models it recovers, justifies, and generalizes the known results. The calculation emphasises the appearance of new dynamical order parameters.